Generally speaking, binocular stereo imaging requires at least two viewpoints, which may need to be spatially distant from one another for large distances between a viewer and an object.
Photographs taken by satellite can be obtained over the interne, revealing a great deal of information in a two-dimensional format. However, obtaining three-dimensional information is useful in such areas as agricultural forecasting, environmental monitoring, forensics, intelligence gathering, object detection (including detection of camouflaged objects using three-dimensional data), target acquisition, remote mapping, and the like.
The unaided eye partially uses photometric stereo methods of depth profiling, in addition to binocular stereo methods, to acquire depth perception. Realistic presentation of images as perceived by the unaided eye is needed in visualization software and training material, which therefore should include photometric stereo information in addition to binocular stereo information. Photometry relates to the measurement of light, in terms of its perceived brightness to the human eye, as distinguished from radiometry, which is the science of measurement of radiant energy (including light) in terms of absolute power. In photometry, the radiant power at each wavelength is weighted by a luminosity function (a.k.a. visual sensitivity function) that models human brightness sensitivity. Photometric stereo, as used herein, is a technique in computer vision for estimating the surface normals of objects by observing that object under different lighting conditions. A surface depth profile value can be calculated when using stereo methods.
Methods relating to the determination of depth and/or surface depth profile from the optical field are described in J. R. A. Torreão, “Natural Photometric Stereo,” Anois do IX Sibgrabi, 95-102 (October 1996) and J. R. A. Torreão and J. L. Fernandes, “Matching photometric stereo images”, J. Opt. Soc. Am., A15(12), 2966-2975, (1998), both of which are hereby incorporated by reference.
The article entitled “Natural Photometric Stereo” discusses the human brain's ability to infer shape from the binocular fusion of some kinds of monocular images. Photometric stereo (PS) images have been observed which are monocular images obtained under different illuminations, that produce a vivid impression of depth, when viewed under a stereoscope. According to the article, the same is true of pairs of images obtained in different spectral bands. The “Natural Photometric Stereo” discusses employing an optical-flow based photometric stereo algorithm; a type of “colour” separated images, which have been so produced as to emulate the kinds of records generated by the photosensitive cells in the human retina, to obtain depth estimates from them. The “Natural Photometric Stereo” article speculates on the possibility that a process similar to PS could work on the human visual system. A natural photometric stereo process is postulated in the “Natural Photometric Stereo” article, invoking some physical and biological arguments, along with experimental results, in support thereof.
In the article entitled “Matching photometric stereo images,” a process of shape estimation is introduced through the matching of photometric-stereo images, which are monocular images obtained under different illuminations. According to the “Matching photometric stereo images” article, if the illumination directions are not far apart, and if the imaged surface is smooth, so that a linear approximation to the reflectance map is applicable, the disparities produced by the matching process can be related to the depth function of the imaged surface through a differential equation whose approximate solution is can be found. The “Matching photometric stereo images” article presents a closed-form expression for surface depth, depending only on the coefficients of the linear-reflectance-map function. If those coefficients are not available, a simple iterative scheme still allows the recovery of depth, up to an overall scale factor.
Various articles have been written on the spatial arrangement of objects and depth perception. In the publication by B. K. P. Horn and B. G. Schunk, “Determining Optical Flow”, MIT Artificial Intelligence Laboratory, 572, 0-27 (1980)(Horn and Schunk article), hereby incorporated by reference, there is a description of a method for finding optical flow, which is defined in the Horn and Schunk article as:                Optical flow is the distribution of apparent velocities of movement of brightness patterns in an image. Optical flow can arise from relative motion of objects and the viewer [citation omitted]. Consequently, optical flow can give important information about the spatial arrangement of the objects viewed and the rate of change of this arrangement [citation omitted].        Discontinuities in the optical flow can help in segmenting images into regions that correspond to different objects.        
According to the Horn and Schunk article, in general optical flow cannot be computed locally, since only one independent measurement is available from the image sequence at a point, while the flow velocity has two components. A second constraint is needed. A method for finding the optical flow pattern is presented in the Horn and Schunk article which assumes that the apparent velocity of the brightness pattern varies smoothly almost everywhere in the image. An iterative implementation is shown which successfully computes the optical flow for a number of synthetic image sequences. The algorithm used in Horn and Schunk article reportedly can handle image sequences that are quantized rather coarsely in space and time and is, reportedly, insensitive to quantization of brightness levels and additive noise. Examples are included where the assumption of smoothness is violated at singular points or along lines in the image.
In light of the above, there exists a need to obtain three-dimensional information about an object from existing two-dimensional images, such as photographic prints, without the need to return to a given viewpoint to obtain further information.